Question: solve the question with steps or explanation 1. Suppose {V,, V2) is a linearly independent set in R . Prove that (v , v, +v,

solve the question with steps or explanation

1. Suppose {V,, V2) is a linearly independent set in R" . Prove that (v , v, +v, , is also linearly independent. 2. Suppose v , V2, v, are distinct points on one line in R" . The line need not pass through the origin. Prove that { V,, V,, v;) is a linearly dependent set. 3. Let T: R" -> R" be a linear transformation and let { V,, V2, vy; be a linearly dependent set in IR" . Prove that the set {TV,, Tv2, Tv;) is linearly dependent

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